Math Questions

Question

Two cards is drawn from a standard deck of cards with replacement.  What is the probability that the first is a king and second is not a king?

 

Two cards are drawn from a standard deck of cards without replacement.  What is the probability that the first is a king and the second is not a king?

 

 

Answer 1

(With replacement: when you draw the second card after having put back the first card, so that you are still drawing from a 52-card deck the second time)
The probability of the first card being a king is 4/52. If you put the first card back before drawing again, then the probability of not getting a king is 48/52. 
Then you multiply 4/52 by 48/52 to get the answer.

 

(Without replacement: when you draw the second card without having put back the first card, so that you are drawing from a 51-card deck the second time) 

The probability of the first card being a king is 4/52. 

The second time you draw, the deck has only 51 cards and 3 kings left, so 48 cards are non-kings. The probability of not getting a king the second time is 48/51. 

Then you multiply 4/52 by 48/51 to get the answer. 

Answer 2

first is a king: 4 kings out of 52 cards means 4/52=1/13

second not a king: 48 cards are not kings out of 52 cards (with replacement) means 48/52=12/13

(1/13)(12/13)=12/169

 

first is a king: 4/52=1/13

second is not a king: 48/51=16/17 (without replacement)

(1/13)(16/17)=16/221